Counterfactuals 2.0 Logic, Truth Conditions, and Probability

The present thesis focuses on counterfactuals. Specifically, we will address new questions and open problems that arise for the standard semantic accounts of counterfactual conditionals. The first four chapters deal with the Lewisian semantic account of counterfactuals. On a technical level, we contribute by providing an equivalent algebraic semantics for Lewis' variably strict conditional logics, which is notably absent in the literature. We introduce a new kind of algebra and differentiate between local and global versions of each of Lewis' variably strict conditional logics. We study the algebraic properties of Lewis' logics and the structure theory of our newly introduced algebras. Additionally, we employ a new algebraic construction, based on the framework of Boolean algebras of conditionals, to provide an alternative semantics for Lewisian counterfactual conditionals. This semantic account allows us to establish new truth conditions for Lewisian counterfactuals, implying that Lewisian counterfactuals are definable conditionals, and each counterfactual can be characterized as a modality of a corresponding probabilistic conditional. We further extend these results by demonstrating that each Lewisian counterfactual can also be characterized as a modality of the corresponding Stalnaker conditional. The resulting formal semantic framework is much more expressive than the standard one and, in addition to providing new truth conditions for counterfactuals, it also allows us to define a new class of conditional logics falling into the broader framework of weak logics. On the philosophical side, we argue that our results shed new light on the understanding of Lewisian counterfactuals and prompt a conceptual shift in this field: Lewisian counterfactual dependence can be understood as a modality of probabilistic conditional dependence or Stalnakerian conditional dependence. In other words, whether a counterfactual connection occurs between A and B depends on whether it is "necessary" for a Stalnakerian/probabilistic dependence to occur between A and B. We also propose some ways to interpret the kind of necessity involved in this interpretation. The remaining two chapters deal with the probability of counterfactuals. We provide an answer to the question of how we can characterize the probability that a Lewisian counterfactual is true, which is an open problem in the literature. We show that the probability of a Lewisian counterfactual can be characterized in terms of belief functions from Dempster-Shafer theory of evidence, which are a super-additive generalization of standard probability. We define an updating procedure for belief functions based on the imaging procedure and show that the probability of a counterfactual A > B amounts to the belief function of B imaged on A. This characterization strongly relies on the logical results we proved in the previous chapters. Moreover, we also solve an open problem concerning the procedure to assign a probability to complex counterfactuals in the framework of causal modelling semantics. A limitation of causal modelling semantics is that it cannot account for the probability of counterfactuals with disjunctive antecedents. Drawing on the same previous works, we define a new procedure to assign a probability to counterfactuals with disjunctive antecedents in the framework of causal modelling semantics. We also argue that our procedure is satisfactory in that it yields meaningful results and adheres to some conceptually intuitive constraints one may want to impose when computing the probability of counterfactuals

Truthmakers, Incompatibility, and Modality

This paper introduces a new framework, based on the notion of compatibility space, obtained by adding a primitive incompatibility relation to a state space in the sense of Fine. The key idea inspiring the framework is to modify Fine's truthmaker semantics by taking the notion of incompatibility as primitive, and use it to define other notions. We discuss some interesting features of the framework and explore its advantages over the standard framework of state spaces. We review some applications of the framework, including proofs of soundness and completeness theorems for a number of logics, one way to use compatibility states to mirror Kripke frames, and an exploration of a way to use the new framework to provide truthmaking clauses for modal formulas

Causal Modeling Semantics for Counterfactuals with Disjunctive Antecedents

This paper applies Causal Modeling Semantics (CMS, e.g., Galles and Pearl 1998; Pearl 2000; Halpern 2000) to the evaluation of the probability of counterfactuals with disjunctive antecedents. Standard CMS is limited to evaluating (the probability of) counterfactuals whose antecedent is a conjunction of atomic formulas. We extend this framework to disjunctive antecedents, and more generally, to any Boolean combinations of atomic formulas. Our main idea is to assign a probability to a counterfactual ( A ∨ B ) \u3e C at a causal model M by looking at the probability of C in those submodels that truthmake A ∨ B (Briggs 2012; Fine 2016, 2017). The probability of p (( A ∨ B ) \u3e C ) is then calculated as the average of the probability of C in the truthmaking submodels, weighted by the inverse distance to the original model M. The latter is calculated on the basis of a proposal by Eva et al. (2019). Apart from solving a major problem in the research on counterfactuals, our paper shows how work in semantics, causal inference and formal epistemology can be fruitfully combined

Developmental ideotype in the context of the dual-purpose use of triticale, barley and durum wheat

Phenology strongly affects the performance of dual-purpose (forage plus grain) cereals by defining the rate of leaf and tiller appearance, the duration of the pre-grazing period and anthesis date. Here, the combined effect of genotypic and environmental variation conditions on anthesis date and the pre-grazing period in durum wheat, triticale and barley was analysed to define a developmental ideotype for their dual-purpose use. The extensive variation for the Haun stage reached at the time of apex emergence from the soil surface was associated with variation in the final leaf number, regardless of environment, species and cultivar. The timing of the terminal spikelet stage was the best predictor of apex emergence. The durum wheats tillered poorly, whereas the barleys and the triticales performed comparably in three of the four environments. In general, the higher the final leaf number, the higher the number of leaves and tillers produced by the time of apex emergence, the higher the number of leaves which emerges subsequently. The development of a high number of leaves both before and after apex emergence is advantageous, provided that anthesis is not overly delayed such that flowering and grain fill occur within a period where stressful conditions are likely to occur. Barley developed many leaves and had a low phyllochron, so was identified as the species with the development best suited for dual-purpose cropping. However, the near simultaneous emergence of the first two tiller apices exposes it to a risk of grazing damage

A Chlamydomonas-derived Human Papillomavirus 16 E7 vaccine induces specific tumor protection.

BackgroundThe E7 protein of the Human Papillomavirus (HPV) type 16, being involved in malignant cellular transformation, represents a key antigen for developing therapeutic vaccines against HPV-related lesions and cancers. Recombinant production of this vaccine antigen in an active form and in compliance with good manufacturing practices (GMP) plays a crucial role for developing effective vaccines. E7-based therapeutic vaccines produced in plants have been shown to be active in tumor regression and protection in pre-clinical models. However, some drawbacks of in whole-plant vaccine production encouraged us to explore the production of the E7-based therapeutic vaccine in Chlamydomonas reinhardtii, an organism easy to grow and transform and fully amenable to GMP guidelines.Methodology/principal findingsAn expression cassette encoding E7GGG, a mutated, attenuated form of the E7 oncoprotein, alone or as a fusion with affinity tags (His6 or FLAG), under the control of the C. reinhardtii chloroplast psbD 5' UTR and the psbA 3' UTR, was introduced into the C. reinhardtii chloroplast genome by homologous recombination. The protein was mostly soluble and reached 0.12% of total soluble proteins. Affinity purification was optimized and performed for both tagged forms. Induction of specific anti-E7 IgGs and E7-specific T-cell proliferation were detected in C57BL/6 mice vaccinated with total Chlamydomonas extract and with affinity-purified protein. High levels of tumor protection were achieved after challenge with a tumor cell line expressing the E7 protein.ConclusionsThe C. reinhardtii chloroplast is a suitable expression system for the production of the E7GGG protein, in a soluble, immunogenic form. The production in contained and sterile conditions highlights the potential of microalgae as alternative platforms for the production of vaccines for human uses

Affinity purification of the E7GGG-FLAG protein.

<p>Oriole-stained gel and Western blot of 10 µl of the following samples, a: E7GGG-FLAG soluble extract before affinity purification; b: column flow-through; c: column wash fraction; d: fraction eluted with 1 M Arg-HCl pH 3.5. M = molecular weight marker.</p